Epitaxial Growth in coherent, strained, asymmetric alloy films$^2$
Abstract Book of the XXIII IUPAP International Conference on Statistical Physics, Genova, Italy, (9-13 July 2007)Abstract
We examine the linear stability/ instability of an epitaxially grown
coherent thin alloy film. Misfit stresses produce morphological instability
in a dislocation-free thin film. The stability of the film's surface is
affected by the coupling between the morphological and alloy segregation instabilities if the
temperature and composition of the
alloy is within the spinodal. An earlier$^3$ nonequilibrium continuum
model is extended to nonsymmetric binary alloys. In the model,
film- substrate misfit strain $\epsilon$, solute expansion coefficient
$\eta$, growth velocity $V$ and growth temperature $T$ are important
parameters that determine the film stability. The asymmetry of the binary
alloy, as represented by the mean order parameter $\phi_o$
($\phi_o = 2 c_o - 1$, $c_o$ is mean concentration) and the dependence
of elastic moduli $E$ and $\mu$ on the fluctuations $\phi$ are
also important. While $\phi(x, \tau)$ is a measure of the
segregation instability, the morphological instability is monitored
through the fluctuations of the film thickness $h(x, \tau)$
around its mean value $h(\tau) = V \tau$.
We find that for $T < T_c$ where $T_c$ is the mean field critical temperature, the system is linearly
unstable at all values
of $\phi_0$ (for $GaAsN$ films grown on $GaAs$ substrate, $T=600K$
and $T_c=12990K$). The morphological instability is affected by the
growth velocity even for small $\epsilon$ and the system remains linearly
unstable as $\phi_0$ moves from the spinodal to the metastable region of
the mean field phase diagram. For $=0$, the morphological
instability is absent and high values of $V$ suppress
compositional instability as a deposited layer is buried before the
surface diffusion has a chance to segregate the two components. However
for $0$, large $V$ enhances the coupled instability. The
surface diffusion in solid alloy films is an activated process and the
time scale for diffusion becomes exponentially large at lower
temperatures. Since surface diffusion plays a central role in the coupled
phase segregation and morphological instability, the time scales for the
evolution of $\phi(x, \tau)$ and $h(x, \tau)$
can become very large in some systems, enabling an experimentalist to grow
relatively flat films of uniform composition $\phi_0$ at low $T$.
We determine the growth velcity $V_o (\phi_o)$ for which the coupled
instability is minimised. For $V=V_o$ the phase segregation instability is just suppressed by the deposition. Our results in the multi-parameter space could provide some guidelines for growing flat films and also to exploit the coupled instability in the alloy film to form self assembled nano-structures. \\
$^2$~Supported by NSERC of Canada. \\
$^3$ F. Léonard and R. C. Desai, Phys. Rev. B57, 4805 (1998);
Appl. Phys. Lett. 74, 40 (1999). Z.-F. Huang and R. C. Desai,
Phys. Rev. B65, 195421 and 205419 (2002).